"What asset backs dollars?"
USD are mostly backed by T-Bills, i.e. government bonds, i.e. the faith you have in the US government (i.e. people of the US) to pay you back. Oddly - they are priced in dollars creating a really odd circular dependency. If the US government paid off all of it's debt today, most currency would be sucked out of the market! :)
Since 2008 - some of USD is backed by crappy real-estate.
Euros are backed by 'strong assets' for the most part: real estate, high grade bonds (I think) etc..
The reason the Euro is a very strong currency is because none of the European countries trust each other to not print money willy nilly. So if a bank wants Euros, they have to put up good collateral. This is how Germans know their Euros are not going to devalued by Italians at the printing press.
RMB is backed by nothing really, just faith in the Chinese government, which is why people don't want to hold them. If China wants to become a real player they have to have transparency, which means they cant print money willy nilly, which means they lose some crazy monetary control they have today. But they think they need that super money power to 'centrally manage' the economy. You can't have both. They either need to have a currency with more integrity - which other nations will 'buy into' - or - they can keep their currency kind of a fiction, but which allows them to turn their economy on a dime if they need to. (Question is, will they turn it in the right direction?).
If Bitcoin were used broadly in some areas - say across a bunch of S. American countries that don't trust their governments, and it was widely used by the citizens, then it might actually have more integrity than say the RMB. Bitcoins cannot be arbitrarily devalued, whereas RMBs are quite often.
The big risk with Bitcoin is that people stop needing/wanting them and they become worthless. Remember that humans are susceptible to up and down 'manias'. All it takes is one rumour and selloff to wipe out Bitcoin for good. If there is a really bad report about US economy, the dollar might go down - but there is 'underlying support' for the USD - people still need them to do commerce, pay taxes. With bitcoins ... a single downturn would wipe them all out for good. They'd have no reason to come back.